Large Deviation Principle for Multi-Scale Stochastic Systems with Monotone Coefficients

The Freidlin–Wentzell’s large deviation principle is established for a class of multi-scale stochastic models involving slow–fast components, where the slow component has general monotone drift and the fast component has dissipative drift driven by multiplicative noise. Our result is applicable to various slow–fast stochastic dynamical systems such as stochastic porous media equations, stochastic p-Laplace equations and stochastic reaction–diffusion equations. The weak convergence method and the technique of time discretization are used to establish the Laplace principle (equivalently, large deviation principle) under the multi-scale framework.